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5.5 Roots of Real 5.5 Roots of Real NumbersNumbers
n bindex
radicand
radical sign
Note: square root when index is not visible
Square RootSquare Root
valuevalue squaresquare square square rootroot
55 (5)(5)22 = 25 = 25
-3-3 (-3)(-3)22 = 9 = 9
25 5
9 3
The inverse of squaring a valueThe inverse of squaring a value
The nThe nthth root root
if , then n na b b a
valuevalue nnthth power power nnthth root root
33 (3)(3)33 = 27 = 27
-2-2 (-2)(-2)55 = -32 = -32
3 27 3
5 32 2
Principal RootPrincipal Root
valuevalue nnthth root root principal principal rootroot
6
3
When there is more than 1 real root, When there is more than 1 real root, the nonnegative rootthe nonnegative root
36
3 27 3
6
The nThe nthth root root if , then n na b b a
nn
eveneven --------------------
oddodd --------------------
eithereither ------------------ --------------------
1+ and 1- root
49 7
b is neg.(-)b is pos.(+) b is 0
no real root
25
3
1 + root
8 25
1- root
32 2
n
1real root
0 0
ensures a nonnegative resultensures a nonnegative result
2 1( 5) ( 5) 5
** : ( ) ( )nNote even power odd power
6 3( 2) ( 2) 8 8